I have compared two different methods for aligning images: Chae’s IDL procedure and Kalle’s / my center of mass Python procedure.

The example given here is the result for a stack of 11 images obtained within 0.7 minutes on JD2455864 in the V-filter, and it is representative for many other similar stacks.

I have aligned the stack with each of the two methods, determined the standard deviation of the stack and divided this with the coadded image of the stack. Finally the image has been multiplied with 100, so that it directly shows the relative error on the raw observation in percent. The images are basically the dO/O in the error budget equations.

The left images are aligned with Chae’s method and the right images are aligned with the center of mass method. The only difference between top and bottom images is the scaling. The top ones are shown on a square root squale that emphasizes the bright side of the Moon, and the bottom images are shown on a histogram equalized scale that emphasizes the dark side of the Moon.

The center of mass method out-performs Chae’s method for both the bright and the dark side. This is especially true for the earthshine. Both methods have difficulties with the bright limb.

The difference between the two methods is not so much the method for calculating the required offset. Instead it is the interpolation technique used in the subpixel move that matters. Chae’s method (shift_sub) uses bilinear interpolation, whereas the CM method uses exponential functions as the interpolating functions. With the CM method there is visible blurring of the lunar features, and it is this smoothing that lowers the standard deviation of the individual pixels.

In the form the methods have now, I would recommend Chae’s alignment whenever we wish to show a nicely centered pretty Moon image and the CM method whenever we wish to determine the intensity of a box of pixels on the Moon. Ofcourse we can play with the parameters of both methods and this might increase or decrease the blurring.

@Peter: Yes, it is definitely possible to calculate the offsets with the CM method and then translate the images with Chae’s shift_sub. The images are then nicely centered and unblurry. However, the standard deviations are then similar to those from a pure Chae alignment, and we could have had the same result with a well-centered reference image.

I have also tried calculating the offset with Chae’s alignoffset and then tranlated the images with Kalle’s interpolation technique. This gives almost as nice and low standard deviations as is the case for a pure CM alignment.